A car travels from one town to another at a speed of 32 mph. If it had gone 4 mph faster, it could have made the trip in 1/2 hr less time. How far apart are the towns?
So far I have this.
speed= distance/time so, letting d be the distance between the two towns, in miles, and t be the time, in hours, for the trip, 32= d/t.
If "it had gone 4mph faster" its speed would have been 32+ 4= 36 and "it could have made the trip in 1/2 hr less time" so the time would be t- 1/2. Now "speed= distance/time" so 36= d/(t+1/2).
32= d/t is the same as d= 32t.
36= d/(t+1/2) is the same as d= 36(t+1/2)= 36t+ 18.
d= 32t= 36t+ 18.
32t = 36t + 18
-32t = 36t - 32t -18
-18 = 4t
-18/4 = 4t/4
-4.5 = t
d=32t
d= 32(-4.5)
d= -144
I don't belive that I should be getting a negative number for the answer. Please help.
So far I have this.
speed= distance/time so, letting d be the distance between the two towns, in miles, and t be the time, in hours, for the trip, 32= d/t.
If "it had gone 4mph faster" its speed would have been 32+ 4= 36 and "it could have made the trip in 1/2 hr less time" so the time would be t- 1/2. Now "speed= distance/time" so 36= d/(t+1/2).
32= d/t is the same as d= 32t.
36= d/(t+1/2) is the same as d= 36(t+1/2)= 36t+ 18.
d= 32t= 36t+ 18.
32t = 36t + 18
-32t = 36t - 32t -18
-18 = 4t
-18/4 = 4t/4
-4.5 = t
d=32t
d= 32(-4.5)
d= -144
I don't belive that I should be getting a negative number for the answer. Please help.